Let $A$ and $B$ be two media. Let $\alpha$ be the angle of incidence of light on medium $B$ and let $\beta$ be the angle of refraction. Let $_{_{A}}n_{{_B}}$ be the refractive index of $B$ with respect to $A$.
We know that $_{_{A}}n_{{_B}} = \dfrac{\sin\alpha}{\sin\beta}$
$_{_{A}}n_{{_B}}$ can also be expressed in terms of the speed of light in $A$ and $B$.
Let the speed of light in $A$ be $c_{_{A}}$ and in $B$ be $c_{_{B}}$
So, $_{_{A}}n_{{_B}} = \dfrac {c_{_{A}}}{c_{_{B}}}$
As the refractive index is a constant, this means that both the values of the refractive index must be the same.
This means that for any two media, the ratio of the sines of the angles of incidence and refraction will be equal to the ratio of the speed of light in both the media.
Is there some proof other than experimental proof for this?
How was it discovered?